A381607 For any nonnegative integer n with ternary expansion Sum_{k >= 0} t_k * 3^k, a(n) = Sum_{k >= 0} t_k * A000045(2*k + 2).

0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 21, 22, 23, 24, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 43, 44, 45, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54

Offset: 0

Author

Rémy Sigrist, Mar 01 2025

Keywords

• nonn
• base
• easy

Comments

Every nonnegative integer appears in the sequence, a finite number of times.

Examples

			42 = 3^3 + 3^2 + 2*3^1, so a(42) = A000045(8) + A000045(6) + 2*A000045(4) = 21 + 8 + 2*3 = 35.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560

Crossrefs

See A022290 for a similar sequence.

Cf. A000045, A028898, A381579.

Programs

PARI

a(n) = { my (t = Vecrev(digits(n, 3))); sum(k = 1, #t, t[k] * fibonacci(2*k)); }

Formula

a(A028898(A381579(n))) = n.